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Surface crystallographySurface crystallographyStructures and notationStructures and notation
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What we want to know: Surface unit cell (periodic structures) Atom positions in unit cell Morphology (steps, islands,domains) Defects
Finally we should connect:
Growth <=> Structure <=> Properties
Surface crystallographySurface crystallographyHow we can do it:
Real space / local probes:
Scanning Tunneling Microscopy (STM)
Atomic Force Microscopy (AFM)
Reciprocal space / global probes:
Low Energy Electron Diffraction (LEED)
Reflectance High Energy Electron Diffraction (RHEED)
Grazing Incidence X-ray Diffraction (GIXD,SXRD)
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g a1
g a1
g a1
g a1
g a1
Crystal lattices at surfaces3D symmetry broken at surfaces => 14 bravais lattices in 3-Diminsions are replaced by 5 bravais lattices in 2 Dimensions
3D bravais lattices 2D Bravais lattices a2
oblique
rectangular
centered rectangular
a2
a2
a2
Square
a2
Hexagonal
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Determination of Miller Indices (fcc)Determination of Miller Indices (fcc)
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Different planes of fcc (faced cubic Different planes of fcc (faced cubic centered)centered)
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Hexagonal closed packed (hcp)Hexagonal closed packed (hcp)
Four index Miller notation ( a1a2a3c ) ( n/h : n/k : n/i: n/l) Index i is redundant: n/h+ n/k= -n/i hcp(0001) and fcc(111) differ only in registry of third-layer
- Result from simple slice cutting a crystal in arbitrary direction (all atoms remain in their exact bulk positions). Alternative names: bulk-terminated, bulk-truncated surfaces
- Low-index: cut crystal along directions with close-packed planes, (100) / (110) / (111)
- High-index: all other cut directions
Hexagonal systems:
Ideal surfaces:
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Hexagonal closed packed (hcp)Hexagonal closed packed (hcp)
Four indices: (a) hcp(0001), (b) hcp(1010)Stacking sequence of hcp(0001) vs. fcc(111): AbAb…. vs. ABCABC…
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fcc(100)
primitive surface unit cell
from conventional bulk unit cell
Common lowCommon low--index planesindex planes
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Some bulk planes + surface structuresSome bulk planes + surface structuresWhen we name bulk planes we still use (hkl):
fcc(100) fcc(111)
Square Bravais lattices Hexagonal Bravais lattice
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Some bulk planes + surface structuresSome bulk planes + surface structuresbut we can now add additional structure on top (red atoms):
fcc(100) fcc(111)
Square bravais lattices Hexagonal bravais lattices
we must be able to clasify these overlayer structures, as Bravais lattices is not enough...
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b1 a1
q
q b2 a2
Surface structure: Woods TerminologySurface structure: Woods TerminologyWood, J. App. Phys. 35, 1306 (1964) Park, Madden Surf. Sci. 11, 188 (1968)
Surface structures are described with respect to the original bulk crystal surface unit cell.
Definition of woods terminology: When it does not work:
Woods terminology can only be used when b1 and b2are rotated through the same angle q with respect to a1 and a2. A more general terminology express the relationship between overlayer and bulk surface as 2x2 matrices:
a1,a2- vectors of bulk surface unit cell
b1,b2- vectors of overlayer unit cell
Structure is described as: b1 =
m11a1+m12a2
m21a1+m22a2 b2
"p" or "c" denotes primitive or centered surface lattice, and X is the chemical symbol of an adsorbed species
The substrate net is therefore denoted: "(1 x 1)".
Matrix notation is VERY rarely used - often the Woods term of a overlayer with close resemblance to the probematic structure is used
To understand the notation let us apply it to the structures from before...
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b2 a2 a1 b1
Some bulk planes + surface structuresSome bulk planes + surface structuresNaming structures with woods terminology:
fcc(100)
a1,a2- vectors of bulk surface unit cell
b1,b2- vectors of overlayer unit cell
"p" or "c" denotes primitiv or centered surface lattice, and X is the chemical symbol of the adsorbed species
The structure is: p(2x2)
Usually however the p will be omitted thus it will be written: (2x2)
AM
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Some bulk planes + surface structuresSome bulk planes + surface structuresNaming structures with Woods terminology:
fcc(100) fcc(111), hcp(0001) (2x2) (1x1) c(2x2) (2x2) (1x1) (√3x√3)R30°
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Simple, coincidence, incommensurate Simple, coincidence, incommensurate
The determinant of M can be used to characterise the relationship between the surface & substrate lattice.
If det M is an integer the lattice is termed simple. If det M is a rational fraction the lattice is coincident. If det M is neither then the adsorbate lattice is incommensurate.
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Examples of WoodExamples of Wood‘‘s Notationss Notations
Masel, „Principles of Adsorption… „p.80-82
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Examples of WoodExamples of Wood‘‘s Notationss Notations
Masel,„Principles of Adsorption… „p.80-82
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Examples of WoodExamples of Wood‘‘s Notations Notation
Masel, „Principles of Adsorption… „ p.80-82
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Face centered cubic (fcc)
0 0 1
5 5 4 1
50 10 1.20 Perspective
Glossy balls blue Show image
VISUALIZE FORM RESET FORM
SURFACE EXPLORER SURFACE EXPLORER Version 2, based on Version 2, based on BALSACBALSAC, (C) , (C) Klaus HermannKlaus Hermann (FH(FHI) I)
Input Form :
Lattice type:
Miller indices: h k l
Size: N1 N2 N3 Ninit
View: Theta Phi Magnf
Design: Color:
HELP
For questions contact Klaus Hermann (scientific) or Fritz Rammer (technical)
http://w3.rz-berlin.mpg.de/~rammer/surfexp_prod/
Make your ownsurfaces...
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Page 1 of 2 SURFACE EXPLORER Output SURFACE EXPLORER
Output
Selection
Lattice type Face centered cubic (fcc) Miller indices 0 0 1 Size 5 5 4 1 View 50 10 Perspective Color blue Design Glossy balls Magnification 1.20
View
http://w3.rz-berlin.mpg.de/~rammer/surfexp_prod/
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Surface specific Surface specific structuresstructures
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Classification of Adsorption sites Classification of Adsorption sites on fcc(111) or hcp(0001)on fcc(111) or hcp(0001)
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Bulk-truncated surface Examples: in reality, none. Alkali halides come close (e.g., KF)
Reconstructed surface
Relaxed surface: in-plane structure is the same as for the bulk-truncated surface
inward relaxationoutward relaxation
1st layer:
2nd layer:
Examples:Au(111) Rh(110) Si(111)
Examples: Ag(111) Ag(110) Cu(111)
Surface relaxations and reconstructions Surface relaxations and reconstructions
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Dangling Bonds in Si, Ge, C, GaAs (spDangling Bonds in Si, Ge, C, GaAs (sp3 3 Hybrid)Hybrid)
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Silicon (001) ReconstructionSilicon (001) Reconstruction
Two neighboring surface atoms move closer to form a “dimer bond”
Each surface atom now has one dangling bond instead of two
Surface unit cell
0.8 Å2.3 Å5.4 Å
Over et al. Phys. Rev. B 55 (1997) 4731
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Bulk Si: diamond structureCut in the (111) plane
STM image
Most prominent example: Most prominent example: The (7 x 7) reconstruction of the Si(111) surfaceThe (7 x 7) reconstruction of the Si(111) surface
DAS (Dimer-Adatom-Stacking-fault) model
Takayanagi, Tanishiro, Takahoashi, Takahashi; Surf. Sci. 164 (1985) 367 S
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Over et al. Phys. Rev. B 48 (1993) 15353
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[001] n
Stepped surfaces Stepped surfaces
Terraces, steps and kinks resemble low-index planes
α
steps
(335) (11 13 19)
n atoms wide (hkl) terrace & (hkl) step kinks
Correspondence between Miller indices and step notation not trivial!
Low miscut surfaces often called vicinal surfaces
Alternative description:
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Simple adsorption sites on (100), (110) and (111)
- Adsorbates can form ordered overlayers, islands, domains
-Coverage is often measured in monolayers 1ML = (#adsorbates/primitive unit cell) = (#adsorbates/surface atom)
- Different reconstructions/overlayers can lead to the same periodicity!
p(2x2)-O p(2x2)-3O
And in extreme cases: facetting…
N-induced clock/anticlock reconstruction
Adsorbate overlayers and induced reconstructionsAdsorbate overlayers and induced reconstructions
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Missing Row Reconstructions on fcc(110): Missing Row Reconstructions on fcc(110): OO--induced reconstruction on Rh(110) induced reconstruction on Rh(110)
H. Over, Prog. Surf. Sci. 58 (1998) 249